By construction CNNs should preserve the translational symmetry if they are fully convolutional. However, this is broken in most cases by the nonperiodic paddings commonly adopted in computer vision tasks. Our models fully preserve the translational symmetry using the periodic boundary condition of the N-body simulation volume. In addition, they approximately preserve the rotational symmetry of the cubic geometry by data augmentations that rotate and reflect the input and output fields as in Ref. [1]}.
